The team had presented a $3.25 million salary to an arbitrator but the case was decided in favor of the four-year veteran who was in his first year of arbitration eligibility.
Happ, 26, had a torrid start to the 2020 season, quickly moving up to the leadoff role for the Cubs. He cooled off late in the year but still produced an .866 OPS in 57 games.
His improvements at the plate began in the second half of 2019 after spending time in the minors earlier that season.
This is the first time under team president Jed Hoyer or former executive Theo Epstein that the team has lost a hearing. The Cubs are now 5-3 all time in arbitration hearings.
Happ was the ninth overall pick of the 2015 draft, breaking into the big leagues two years later. He's expected to hit leadoff again and play center field this season.
MLB.com was first to report Happ had won his case.